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On Source Terms and Boundary Conditions Using Arbitrary High Order Discontinuous Galerkin Schemes
This article is devoted to the discretization of source terms and boundary conditions using discontinuous Galerkin schemes with an arbitrary high order of accuracy in space and time for the solution of hyperbolic conservation laws on unstructured triangular meshes. The building block of the method is a particular numerical flux function at the element interfaces based on the solution of Generalized Riemann Problems (GRPs) with piecewise polynomial initial data. The solution of the generalized Riemann problem, originally introduced by Toro and Titarev in a finite volume context, provides simultaneously a numerical flux function as well as a time integration method. The resulting scheme is extremely local since it integrates the PDE from one time step to the successive one in a single step using only information from the direct side neighbors. Since source terms are directly incorporated into the numerical flux via the solution of the GRP, our very high order accurate method is also able to maintain very well smooth steady-state solutions of PDEs with source terms, similar to the so-called well-balanced schemes which are usually specially designed for this purpose. Boundary conditions are imposed solving inverse generalized Riemann problems. Furthermore, we show numerical evidence proving that by using very high order schemes together with high order polynomial representations of curved boundaries, high quality solutions can be obtained on very coarse meshes.
Michael Ungermann, Jan Lunze and Dieter Schwarzmann
Test signal generation for service diagnosis based on local structural properties
The paper presents a new approach to the generation of test signals used in service diagnosis. The tests make it possible to isolate faults, which are isolable only if the system is brought into specific operating points. The basis for the test signal selection is a structure graph that represents the couplings among the external and internal signals of the system and the fault signals. Graph-theoretic methods are used to identify edges that disappear under certain operating conditions and prevent a fault from changing the system behavior at this operating point. These operating conditions are identified by validuals, which are indicators obtained during the graph-theoretic analysis. The test generation method is illustrated by a process engineering example.
Dynamic monopolies in graphs have been studied as a model for spreading processes within networks. Together with their dual notion, the generalized degenerate sets, they form the immediate generalization of the classical notions of vertex covers and independent sets in a graph. We present results concerning dynamic monopolies in graphs of given average threshold values extending and generalizing previous results of Khoshkhah et al. [On dynamic monopolies of graphs: The average and strict majority thresholds, Discrete Optimization 9 (2012) 77-83] and Zaker [Generalized degeneracy, dynamic monopolies and maximum degenerate subgraphs, Discrete Appl. Math. 161 (2013) 2716-2723].
We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.
Scientific studies have regularly confirmed that nowadays the salt consumption through food is too much, and its consumption has to be reduced. The aim of the study was to ascertain the amount of salt consumed per day by 18–35 year-old Latvians as well as to identify the main sources of salt in their diets. The following research methods were used in the study: questionnaire based on an example recommended by the World Health Organisation, sociological research method, bread baking tests, and logically constructive, and statistical research methods. The results of this research showed that the average intake of salt in the diet of 18–35 year-old Latvians was 7.1 g per day. Of all the respondents, 63% consumed more than the recommended 5 g of salt per day, and none of them consumed less than necessary to meet their physiological needs. The results showed that women consumed less salt than men — approximately 6 g per day, while men consumed 8.2 g of salt per day. The main sources of salt in the diet of 18–35 year old Latvians were cereals and cereal products, as well as meat and meat products. Among cereal products, the key source of salt was represented by bread and pastry.
José D. Alvarado, Simone Dantas and Dieter Rautenbach
For a graph G, let R(G) and yr2(G) denote the Roman domination number of G and the 2-rainbow domination number of G, respectively. It is known that yr2(G) ≤ R(G) ≤ 3/2yr2(G). Fujita and Furuya [Difference between 2-rainbow domination and Roman domination in graphs, Discrete Appl. Math. 161 (2013) 806-812] present some kind of characterization of the graphs G for which R(G) − yr2(G) = k for some integer k. Unfortunately, their result does not lead to an algorithm that allows to recognize these graphs efficiently. We show that for every fixed non-negative integer k, the recognition of the connected K4-free graphs G with yR(G) − yr2(G) = k is NP-hard, which implies that there is most likely no good characterization of these graphs. We characterize the graphs G such that yr2(H) = yR(H) for every induced subgraph H of G, and collect several properties of the graphs G with R(G) = 3/2yr2(G).
Design of security protocols is notoriously error-prone. For this reason, it is required to use formal methods to analyze their security properties. In the paper we present a formal analysis of the Canvas protocol. The Canvas protocol was developed by Harald Vogt and should provide data integrity inWireless Sensor Networks. However, Dieter Gollmann published an attack on the protocol. We consider the fallacy of the Canvas scheme in different models of the attacker and present a solution for correcting the scheme.We propose a formal model of the fixed Canvas protocol in the applied pi-calculus. This model includes a model of the network topology, communication channels, captured nodes, and capabilities of the attacker. Moreover, we formulate and analyze the data integrity property of the scheme in the semantic model of the applied pi-calculus. We prove that the fixed Canvas scheme, in the presence of an active adversary, provides data integrity of messages assuming that captured nodes are not direct neighbors in the communication graph of a sensor network. Finally, we discuss the applicability of the proposed formal model for analysis of other WSN security protocols.